GENERALIZED VARIATIONAL PRINCIPLES FOR VISCOELASTIC THIN AND THICK PLATES WITH DAMAGE

From the constitutive model with generalized force fields for a viscoelastic body with damage, the differential equations of motion for thin and thick plates with damage are derived under arbitrary boundary conditions. The convolution-type functionals for the bending of viscoelastic thin and thick plates with damage are presented, and the corresponding generalized variational principles are given. From these generalized principles, all the basic equations of the displacement and damage variables and initial and boundary conditions can be deduced. As an example, we compare the difference between the dynamical properties of plates with and without damage and consider the effect of damage on the dynamical properties of plates.

LARGE DEFLECTION PROBLEM OF THIN ORTHOTROPIC CIRCULAR PLATE ON ELASTIC FOUNDATION WITH VARIABLE THICKNESS UNDER UNIFORM PRESSURE

Basic equations for large deflection theory of thin orthotropic circular plate on elastic foundation with variable thickness under uniform pressure are derived in this paper. The second opproximation solutions are obtained by means of the modified iteration method. The relation curves of the nondimensional loading and foe deflection, as to the differential ε and μrθ and λ are shown in Figs. 2, 3, 4. In special circumstance, the results are in accordance with those in [1], [6].

CONSTRUCTION OF RECTANGULAR DISPLACEMENT-BASED ELEMENT FOR THICK/THIN PLATES

In this paper,a method of constructing displacement-based elment for thick/thin plates is devel- oped by using the technique of generalized compatibility,and a rectangular displacement-based element with 12 degrees of freedom for thick/thin plates is presented.This method enjoys a good accuracy with simple formulation and is free of shear- locking as the thickness of the plate approaches zero.

NAVIER SOLUTION FOR THE ELASTIC EQUILIBRIUM PROBLEMS OF ANISOTROPIC SKEW THIN PLATE WITE VARIABLE THICKNESS IN NONLINEAR THEORIES

This paper discusses the elastic equilibrium problems of anisotropic skew thin plate of variable thickness simply supported on all four sides in nonlinear theories, and uses the Navier method to seek an approach to the problem, and to illustrate the solution with the examples. In conclusion, the mention is made of the scope of application and the convergency of the solution.

BASIC EQUATIONS OF THE PROBLEM OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE WITH VARIABLE THICKNESS

Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given;then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given.

UNIFORMLY VALID ASYMPTOTIC SOLUTIONS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE OF FOUR CLAMPED EDGES WITH VARIABLE THICKNESS

By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained.

Improved Mechanical Properties of Textile Reinforced Concrete Thin Plate

Textile reinforced concrete （TRC） is especially suitable for the thin-walled and light-weight structural elements with a high load-bearing capacity. For this thin element, the concrete cover thickness is an important factor in affecting the mechanical and anti-crack performance. Therefore, the influences of the surface treatment of the textile and mixing polypropylene fiber into the concrete on the properties of the components with different cover thickness were experimentally studied with four-point bending tests. The experimental results show that for the components with the same cover thickness, sticking sand on epoxy resin-impregnated textile and adding short fiber into the concrete are helpful to improve their mechanical performance. The 2-3 mm cover thickness is enough to meet the anchorage requirements of the reinforcement fiber and the component has good crack pattern and mechanical behavior at this condition. Comparison between the calculated and the experimental Values of flexural capacity reveals satisfactory agreement. Finally, based on the calculation model of the crack spacing of reinforced concrete structures, the crack extension of this thin-wall component was qualitatively analyzed and the same results with the experimental were obtained.

Effect of Deflected Disc's Thickness to the Damping Characteristic of Tube Shock Absorbers

Research is conducted on the relationship between thickness of deflected disc and damping force of tube shock absorbers. By analyzing performing characteristics of the throttling valve using throttling theory of small clearance space and thin place deformation theories, mathematical correlation between disc thickness and magnitude of damping force is formulated. Moreover, a rule concerning change of damping force in terms of disc thickness is concluded.

考虑边界约束影响的充填挡墙厚度确定方法及应力分布规律研究

不合理的边界加固方式会导致充填过程中挡墙边缘抗弯能力弱化进而影响采场安全。基于此,为了确定合理的充填挡墙厚度,探讨边界约束对充填挡墙稳定性的影响,将挡墙结构简化为4类薄板模型。以第一强度准则为判断依据,提出了不同边界约束模式下充填挡墙厚度确定方法。结合大冶铁矿工程实际,探讨了不同边界约束模式下充填挡墙应力分布规律,并通过解析几何和数值模拟对本文理论模型进行了验证。研究结果表明:①挡墙最小厚度与充填高度、充填料浆容重呈正相关关系,与挡墙抗拉强度呈负相关关系,增加挡墙抗拉强度有利于挡墙稳定性;②挡墙内外侧拉伸应力分布存在明显差异,外侧呈X型分布,内侧呈O型分布,边界抗弯能力弱化会导致拉伸区域拓展,增加挡墙边界弯矩可以有效防止挡墙破坏;③数值模拟获取的应力分布规律与解析几何分析结果高度一致,进一步验证了本文充填挡墙厚度确定方法的可靠性,结果可为类似采场充填挡墙参数优化提供参考。

新能源汽车铝电池盒MIG焊接新工艺

在铝合金电池盒实际生产中,由于焊接位置较多、焊接接头板厚差异大,焊接一次合格率很难控制,这就需要研发一种焊接工艺提升铝合金薄厚板焊接的稳定性。目前铝合金电池盒MIG焊接主要是直流脉冲焊接,其中包括直流单脉冲或直流双脉冲焊接。通过分析发现,采用直流+交流摆动同步双脉冲焊接,在相同电流情况下可有效降低焊接热输入,在相同热输入情况下可增加焊缝a值。并在铝合金薄厚板焊接时,可在厚板位置使用直流脉冲,薄板位置使用交流脉冲,保证厚板熔深且薄板不烧穿。摆动同步交直流焊接技术已经在实际生产中得到应用,并有效提高了焊缝合格率和生产效率。

胶结充填体拱效应作用下的水平矿柱回采安全厚度研究

通过建立三维胶结充填体拱应力模型,得到胶结充填体竖向荷载计算公式,并根据四边固支顶板模型和岩体极限抗拉强度准则,得到了水平矿柱回采安全厚度确定方法。在某铅锌矿612采场水平矿柱回采的运用实践表明,解析模型计算的胶结充填体竖向应力与数值模拟结果基本吻合,数值模拟中顶板未出现塑性区,验证了计算确定的保留顶板厚度满足安全生产需求;回采过程监测结果表明,监测点附近的最大累计位移低于极限位移,保留顶板趋于稳定,确定的水平矿柱回采安全厚度具有足够的可靠性。

一种新型厚薄板通用三角形广义协调元

本文提出了一种假设单元剪切应变场的新方法，基于广义协调理论构造了一个只有９个自由度的三角形厚薄板通用单元ＴＣＧＣＴ９。数值算例表明：该单元具有自由度少，精度高，无剪切闭锁现象等特点，适用于从极薄板到厚板较大的范围。

采用面积坐标的四边形厚薄板通用单元

本文采用四边形面积坐标，利用假设剪切应变场方法和广义协调理论构造出一个具有12个自由度的四边形厚薄板通用弯曲单元TACQ。基本思路如下：首先从Mindlin厚板理论出发，独立假设剪应变场和挠度场，而转角场则由挠度场和剪应变场导出；其次，单元剪应变场是先按Timoshenko厚梁理论确定单元各边剪应变，然后在单元内进行合理插值导出；第三，单元挠度场是根据单元角点处挠度的点协调条件以及单元各边挠度和法向转角的平均协调条件导出。这个方法有两个特点，（1）由于满足点协调和边协调的广义协调条件，故能保证收敛；（2）由于在薄板情况剪应变退化为零，故不出现剪切闭锁现象。数值算例表明：该单元具有精度高，收敛性和可靠性好，对网格畸变不敏感，无剪切闭锁现象等优点；适用于从极薄板到厚板较大的范围。

冲击碾压混凝土路面的破碎尺度

我国修建的第一批高速公路有不少是水泥混凝土路面,经过10余年的使用已经进入大修期。安徽省高速公路总公司采用了冲击碾压旧路面加铺水泥混凝土或沥青混凝土工艺大修路面,称为"冲击白+白"和"冲击白+黑"法。破碎后的板块平面尺度最小只有厚度的2～4倍,本文研究说明,与刚性支承板不同,破碎板块弯沉和内力用厚板和薄板理论计算结果很接近;并且讨论了破碎板块平面尺度的可能范围。

基于薄板理论的空区顶板稳定性分析

考虑作用于顶板上的均布载荷及作用于顶板上方中心处的集中载荷情况下,基于四边固支矩形薄板的纳维叶解法,分别导出了均布载荷与集中载荷作用下矩形顶板的挠度方程与应力表达式.分析得到四边固支矩形板在均布载荷和集中载荷作用下的高应力主要出现在板的中心以及长边的中点处,影响应力的因素主要包括厚度、载荷大小、板的尺寸以及泊松比.依据第一强度理论建立均布载荷和集中载荷共同作用下的顶板安全性控制方程,并求解得到其安全临界顶板厚度,并通过工程实例验证了该控制方程的正确性.

中厚板理论的适用范围和精确程度的研究

利用Reissner中厚板理论边界元、Mindlin中厚板理论有限元和三维弹性力学有限元分析了各种厚跨比的板的位移和应力,以确定利用三维理论、中厚板理论和薄板理论分析板时厚跨比的适用范围以及精确程度,为分析板时选择采用薄板理论、中厚板理论还是三维理论提供理论依据;同时也验证了采用缩减积分的Mindlin中厚板理论有限元法缓解了剪切锁死现象.

一种有效的厚薄板壳单元

对于厚薄板壳分析提出了一种有效的拟协调位移型三角形单元．采用Ｍｉｎｄｌｉｎ变形假定，在横向剪切刚度项中引入特殊的罚函数，有效地解除了剪切闭锁和抑制了零能模式，并扩大了对跨厚比的适用范围，计算精度也有明显提高．

一种厚板薄板通用的新型广义协调元

在适用于中厚板的八结点平板弯曲单元基础上 ,通过引入剪应变与位移的广义协调条件 ,建立起一种新型广义协调元 ,不仅保留了原单元适用于中厚板的特点 ,同时对薄板也给出了较精确的解 ,是一种厚板和薄板通用的新型广义协调元。

一个不闭锁和抗畸变的四边形厚板元

构造一个彻底消除剪切闭锁现象并且对网格畸变不敏感的四边形厚薄板通用单元RPAQ。在方法上有三个特点:第一,在厚板挠度和转角的试函数中,采用了合理匹配方案,从而在源头上彻底消除了剪切闭锁现象;第二,采用四边形面积坐标,以代替通常的等参坐标,从而使网格畸变时仍然保持高精度;第三,采用广义协调元做法,使协调条件的采用灵活多样,并保证单元的收敛性。进行了一系列数值例题测试,表明单元RPAQ能自动消除闭锁现象,在由薄板到厚板的不同情况下,在各种网格畸变的情况下,都能体现出良好的精度和数值稳定性。

用迈克尔逊干涉仪测量全息干板膜厚度

全息干板膜的厚度是全息干板的重要参数之一。使用迈克尔逊干涉仪和白光光源对2种全息干板膜厚度进行测量,并对测量结果误差进行分析,给出了测量误差与膜厚及折射率之间的关系以及此方法的适用范围。研究结果表明:在膜厚从8μm增至41μm的过程中,测量结果的绝对误差≤2μm且变化很小,相对误差则从14.1%降到了2.2%。随着膜厚的增加,相对误差明显降低;折射率n也参与了误差传递,其值与测量误差呈类似反比关系;当n值在1.5附近时,为保证测量的准确性,所测膜厚≥40μm。最后指出,迈克尔逊干涉仪在测量全息干板膜等较厚的薄膜时,具有测量范围大,结果较准确等优点。